TY - JOUR
T1 - Self-adjointness and conservation laws of difference equations
AU - Peng, Linyu
N1 - Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2015/6/1
Y1 - 2015/6/1
N2 - A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.
AB - A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.
KW - Conservation laws
KW - Noether's theorem
KW - Symmetries
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U2 - 10.1016/j.cnsns.2014.11.003
DO - 10.1016/j.cnsns.2014.11.003
M3 - Article
AN - SCOPUS:84922771254
SN - 1007-5704
VL - 23
SP - 209
EP - 219
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
IS - 1-3
ER -